1Cademy - Finding the Dimensions of a Rectangular Patio with Area $$180$$ Square Feet

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How to Solve a Quadratic Equation by Factoring

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Finding the Dimensions of a Rectangular Patio with Area $180$ Square Feet

Apply the geometry problem-solving strategy to find the dimensions of a rectangular patio when its area is $180$ square feet and the width is three feet less than the length. Let $l$ represent the length, making the width $l - 3$ . Substitute these expressions into the area formula $A = l \cdot w$ to get $180 = l(l - 3)$ . Distribute to produce $180 = l^2 - 3l$ , and subtract $180$ from both sides to rearrange into the standard quadratic form $0 = l^2 - 3l - 180$ . Factor the trinomial into $(l - 15)(l + 12) = 0$ . By the Zero Product Property, $l = 15$ or $l = -12$ . Since a physical length cannot be negative, discard $-12$ . The length is $15$ feet, and the width is $15 - 3 = 12$ feet.

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Updated 2026-04-30

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OpenStax Intermediate Algebra

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